Modelling elasticity in solids using active cubes - Application to simulated operations

Abstract

This paper describes an approach to elastic modelling of human tissue based on the use of 3D solid active models - active cubes [2] - and a shape description based on the metric tensor in a solid. Active cubes are used because they provide a natural parameterization of the surface and the interior of the given object when deformed to match the object's shape. Using the metric tensor to store the shape of the deformed active cube the elastic behaviour of the object in response to applied forces or subject to constraints is modelled by minimizing an energy based on the metric tensor. The application of this approach to modelling the elastic deformation of human tissue in response to movement of bones is demonstrated.